Gravity gradient measurements can be useful to a geophysicist in prospecting for oil and gas and other minerals. It is well known that various subsurface structures are indicative of mineral deposits, oil, gas, and the like, and that small variations in the gravitational field (gravity gradient) may indicate the presence of subsurface structures.
The relationship between the density of the subsurface structure and the earth's gravitational field can be illustrated by the following formula: ##EQU1## where d is the density of a layer being determined, F is the free air gradient, G is the universal gravitational constant, and .differential.g(z)/.differential.z is the vertical gradient of the earth's vertical gravitational field within the layer.
In the past, various instruments and methods have been developed to measure the vertical gradient of the earth's vertical gravitational field and/or gradients thereof. One prior art method for determining the vertical gravity gradient for well logging purposes requires that a detailed gravity survey be used wherein gravitational field measurements are made at two depths. This is followed by a calculation to generate the gradient. This method of determining the gravity gradient is time consuming and is incompatible with the continuous well logging practices.
The following patents disclose various other prior art methods and apparatus for determining the vertical gravity gradient: U.S. Pat. Nos. 3,630,086; U.S. 3,668,932; and 3,926,054.
Another method for determining the vertical gradient of the gravitational fields is described in U.S. Pat. No. 4,513,618. In this method, the vertical gradient of the vertical gravitational field is determined by producing a signal representative of the vertical gradient only of the vertical gravitational field. This signal is produced by a floating gradiometer in response to the vertical gravitational field. The gradiometer comprises a housing containing a fluid and a float means suspended in the fluid, said float means being the particular component of the apparatus that responds to the vertical gravitational field.
In a floated gradiometer, the forces acting on the float can be described by the following mathematical formula: ##EQU2## where W is the net force on the float, where M is the mass of the float, where .DELTA.z is the difference in position of the center of buoyancy and the center of mass, and where .differential.g(z)/.differential.z is the vertical gradient of the vertical gravity. E(T) is proportional to the difference in the mass of the float and the mass of the displaced fluid times the gravitational acceleration.
In equation 2, the net force on the float is dependent upon two terms. The first term is proportional to the difference in position of a center of buoyancy and the center of mass times the vertical gravity gradient. The second term, which is related to the gravity acceleration force, is proportional to the difference in the mass of the float and the mass of the displaced fluid times the gravitational acceleration.
In the past, in attempting to determine the gravity gradient force, the gravity acceleration force was reduced by carefully adjusting the density of the fluid by varying the temperature and the fluid composition. This balancing is very tedious and exacting and has not been accomplished stably enough for a field instrument.
There is a need for a method of determining the vertical gravity gradient that is compatible with continuous well logging practice and is stable enough for use as a field instrument.